The development comes as Sir Jim Ratcliffe's £1.25bn minority purchase of the club nears completion.
Arnold held different roles at Old Trafford after joining in 2007 but was elevated to the position of chief executive in February 2022 following the exit of Ed Woodward.
General counsel Patrick Stewart will fill Arnold's position on a temporary basis until a permanent replacement is named.
United said in a statement: “Richard Arnold has decided to step down as Chief Executive of Manchester United after 16 years with the club.
“Patrick Stewart will take over as interim CEO, in addition to his existing role as General Counsel, with Richard continuing to provide transitional support until the end of December.
“A search process will be carried out for a new permanent CEO.”
Outgoing chief executive Arnold said: “It has been an incredible privilege to serve this great football club for the past 16 years.
“Through highs and lows, the constant has been the dedication of our employees and fans.
“I would like to thank all of them for their loyalty and commitment, and wish everyone associated with the club the very best for the future.”
United executive co-chairman Joel Glazer said: “I would like to thank Richard for his outstanding service to Manchester United over the past 16 years, and wish him all the best for his future endeavours.
“We are fortunate to be able to call on the deep knowledge and experience of Patrick Stewart to provide interim stability and continuity as we embark on a search for a new permanent CEO.”
